Abstract
It is demonstrated, using a combination of theoretical and experimental computer science, that there is no nine-input sorting network of depth six. If a nine-input sorting network of depth six exists, then there exists one with very special structure. There is an efficient algorithm for constructing and testing comparator networks of this form. This algorithm was implemented and executed on a supercomputer.
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This research was supported by NSF Grant CCR-8801659 and a Research Initiation Grant from the Pennsylvania State University.
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Parberry, I. A computer-assisted optimal depth lower bound for nine-input sorting networks. Math. Systems Theory 24, 101–116 (1991). https://doi.org/10.1007/BF02090393
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DOI: https://doi.org/10.1007/BF02090393